Question

how would i make this into a single logarithm??
3logbase(7)x-(1/4)logbase(7)w+4logbase(7)z??

Answer 1

heres the actuall equation if you dont get my typed ver.
\[3\log _{7}x-\frac{ 1 }{ 4 }\log _{7}w+4\log_{7}z\]

Answer 2

Use the following properties:
\[\large a\log_bc=\log_b\left(c^a\right)\\
\large \log_ba+\log_bc=\log_b(ac)\\
\large\log_ba-\log_bc=\log\left(\frac{a}{c}\right)\]

Answer 3

ok... so i would get \[ \frac{ \log _{7}x ^{3} z ^{4}}{ \log _{7}\sqrt[4]{z} }\]

Answer 4

is that correct?

Answer 5

ahhh i see

Answer 6

that would go to\[\frac{ z ^{\frac{ 19 }{ 4 }} }{ 1 }\]

Answer 7

right?

Answer 8

oh ok now that would go outside the fraction right?

Answer 9

ahhh i see thanks alot :)

Answer 10

Wait, back up a bit. Mistakes have been made! Where did the \(w\) go?

Answer 11

\[\log_7\left(\frac{x^3z^4}{w^{1/4}}\right)\]
This would be your final answer.

Answer 12

oh shoot... its the z in the denomitator =0

Answer 13

ya haha oops... but thanks olot :)

Answer 14

You're welcome!